In order for a fan or prop blade to deflect air backwards, there has to be air where the fan blade is, obviously. A fan pushes air, and pushing is something that requires physical contact.
Wind speed is a measure of the average relative motion of the individual molecules of the air itself: at any given time in an atmosphere there are molecules going every which way at various speeds, but if there are more going one direction than another, or if the ones going that direction tend to be faster, then there is a wind. That's how a fan blade generates wind - it takes the air molecules and shoves them in a particular direction.
"It takes air molecules" is deliberately phrased, because in order for a fan to blow air, it has to get air to blow. Imagine you put your fan into a bucket of water and it starts 'blowing' the water out of the bucket: once the bucket is empty, the fan stops blowing water because there's no more water to blow.
The same thing happens with a fan: if your fan blades are going too quickly, one blade will scoop up all the air and blow it away, but by the time the second blade comes aroung, the only molecules that are there for it to catch are the ones that were already going that direction. Naturally, these are moving at a variety of speeds around an average in that direction, and the faster they're going already, the less energy the fan blade can impart to them. There is then a plateau effect in which there's a maximum speed that the fan blade can push air out, and that speed coincides with the speed of sound in that medium, I.e. the speed the molecules were already going naturally.